Magnetic resonance imaging (MRI) has outstanding soft-tissue contrast and provides unparalleled benefits in various diagnoses. It is an important way of observation in current clinical practice. The scanning period of an MRI, however, is long, which greatly limits the diagnostic efficiency. Obtaining undersampled K-space data through partial scanning at a specific acceleration magnification is a critical approach to save scanning time. Existing approaches only rebuild the K-domain or the image domain alone or alternately process the two domains through serially coupled image domain and K-domain convolution, resulting in poor reconstruction performance. A dual-domain parallel codec structure that processes image domain and K-domain data simultaneously is presented to provide high-quality reconstruction of undersampled K-space data at high acceleration rates. The proposed technique reconstructs the undersampled image domain and K-domain data using two parallel codec networks, respectively, then combines the features of the K-domain branch into the image domain using the inverse Fourier transform, considerably enhancing reconstruction quality. For presampling data with varying acceleration magnifications, experimental results reveal that the proposed method outperforms other U-Net-based image reconstruction methods. This proposed method is projected to develop into a high-performance, high-acceleration-magnification MRI undersampling data reconstruction method that can be used in clinical MRI reconstruction.